Chinese Journal of Chemical Physics  2018, Vol. 31 Issue (1): 33-38

The article information

Ming-li Du, Yu-jie Hu, Jing Huang, Qun-xiang Li

Electronic Transport Properties of Spin-Crossover Magnet Fe(Ⅱ)-N4S2 Complexes
Fe（Ⅱ）-NH(aΔ)N4S2自旋翻转单分子磁体的电子输运性质
Chinese Journal of Chemical Physics, 2018, 31(1): 33-38

http://dx.doi.org/10.1063/1674-0068/31/cjcp1706117

Article history

Received on: June 6, 2017
Accepted on: June 10, 2017
Electronic Transport Properties of Spin-Crossover Magnet Fe(Ⅱ)-N4S2 Complexes
Ming-li Dua, Yu-jie Hua, Jing Huangb, Qun-xiang Lia
Dated: Received on June 6, 2017; Accepted on June 10, 2017
a. Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
b. School of Materials and Chemical Engineering, Anhui Jianzhu University, Hefei 230601, China
*Author to whom correspondence should be addressed. Qun-xiang Li, E-mail:liqun@ustc.edu.cn
Abstract: Spin-crossover (SCO) magnets can act as one of the most possible building blocks in molecular spintronics due to their magnetic bistability between the high-spin (HS) and low-spin (LS) states. Here, the electronic structures and transport properties through SCO magnet Fe(Ⅱ)-N4S2 complexes sandwiched between gold electrodes are explored by performing extensive density functional theory calculations combined with non-equilibrium Green's function formalism. The optimized Fe-N and Fe-S distances and predicted magnetic moment of the SCO magnet Fe(Ⅱ)-N4S2 complexes agree well with the experimental results. The reversed spin transition between the HS and LS states can be realized by visible light irradiation according to the estimated SCO energy barriers. Based on the obtained transport results, we observe nearly perfect spin-filtering effect in this SCO magnet Fe(Ⅱ)-N4S2 junction with the HS state, and the corresponding current under small bias voltage is mainly contributed by the spin-down electrons, which is obviously larger than that of the LS case. Clearly, these theoretical findings suggest that SCO magnet Fe(Ⅱ)-N4S2 complexes hold potential applications in molecular spintronics.
Key words: Electronic structure    Transport property    Spin-crossover magnet    Spin-filtering effect
Ⅰ. INTRODUCTION

Since the first experimental measurement of a single 1, 4-dithiol-benzene molecular junction [1], a single molecule can be stably connected to electrodes using various techniques, such as the mechanically controllable break junction [2], scanning tunneling microscope [3], atomic force microscope [4], and crossed wire tunneling junction method [5, 6], and then various functional molecular devices including molecular wire, switch, rectifier, and negative differential resistance, have been successfully demonstrated [7-10]. In the recent past years, considerable attention has been paid to molecular spintronics [11-13], which combines the contemporary exploitation of the electron and spin degrees of freedom at single-molecule level, since it holds promise for the next generation of electronic devices, especially in high-density information storage and quantum computing. Based on magnetic molecules (i.e. iron phthalocyanine), spin filtering and spin-crossover (SCO) behaviors have been demonstrated experimentally or theoretically [13-16].

It is well known that SCO complexes are the most possible building blocks in molecular spintronics since the bistability between the high-spin (HS) and low-spin (LS) states implies potential application (i.e. the information storage) [17, 18]. In general, such materials are formed by 3d transition metal ions in an octahedral surrounding, which displays a spin transition from a LS state, usually the ground state, to a HS state, usually a metastable one. Such a LS-HS transition can be triggered by diverse external stimulus, such as temperature, light, pressures, magnetic or electric fields or charge flow [19-21]. It is accompanied by a modification of the geometrical structure, which alters the crystal field strength. Among these SCO magnets containing various 3d metal ions, such as Cr(Ⅱ), Mn(Ⅱ), Mn(Ⅲ), Co(Ⅱ), Co(Ⅲ), Ni(Ⅲ), and Fe(Ⅲ) [22], the most extensively investigated SCO transition is between a $^1$A$_{1\textrm{g}}$ LS state and a $^5$T$_{2\textrm{g}}$ HS one in SCO magnet containing an Fe(Ⅱ) ion. Previous experimental and theoretical activities mainly focused on the synthesis, their structures and magnetic properties of the mononuclear Fe(Ⅱ) family with the octahedral Fe(Ⅱ) coordinated to six N atoms (N$_6$), and more attention should be paid for the transport properties through the SCO magnet Fe complexes, although electron transport experiments in SCO complexes at the single molecular level remain scarce so far, since depositing such complexes on surfaces with a controllable anchoring contact is very difficult [23-25].

Till now, it should be pointed out that coordination environments other than N$_6$ are scarce. Very recently, a rare class of SCO magnet Fe(Ⅱ) complexes with the (N$_4$S$_2$) coordination have been successfully prepared in experiments [26], as illustrated in FIG. 1 (a) and (b), in which the Fe(Ⅱ) ion is coordinated by two monodentate N-bound NCBH$_3$$^- ligands and a tetradendete ligand S, S'-bis(2-pydidylmethyl)-1, 2-thioehane (bpte). Namely, four N atoms and two S atoms directly bond to the central Fe(Ⅱ) ion, the equatorial plane of the octahedral coordination is formed by two N atoms of NCBH_3$$^-$ ligands and two S atoms of the thioether of the bpte ligand, while the pyridyl N atoms of the bpte occupy the two axial sites. Here, we explore the SCO transition and transport properties of this novel SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes sandwiched between gold electrodes. Our investigations are carried out by performing extensive density functional theory (DFT) calculations combined with nonequilibrium Green's function (NEGF) technique. The obtained SCO energy barriers can be used to explain the photoswitching between the HS and LS states in experiment. Moreover, we find that the nearly perfect spinfiltering effect appears in this SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state, and the corresponding current under small bias voltage is mainly contributed by the spin-down electrons, which is obviously larger than that of the LS case.

 FIG. 1 (a) Optimized structures of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complex with the LS state, (b) spin density distribution of the magnet with the HS state. (c) The spatial distribution of the HOMO and LUMO of the Fe(Ⅱ)-N$_4$S$_2$ complexes for the LS and HS states.
Ⅱ. COMPUTATIONAL MODEL AND METHOD

Structural, electronic structures, and transport properties of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ are explored by performing DFT calculations combined with NEGF method, implemented in ATK package [27, 28]. In our calculations, the generalized gradient approximation in the Perdew-Burke-Ernzerhof form is used to describe the exchange and correlation energy. The interaction between ionic cores and valence electrons is modeled with Troullier-Martins nonlocal pseudopotential. Single-$\zeta$ plus polarization for Au atoms in electrodes and double-$\zeta$ plus polarized basis sets are employed for all other atoms. An energy cutoff is set to be 150 Ry for the real-space grid on which the Poisson equation is self-consistently solved. The spin-resolved transmission coefficients of these molecular junctions are obtained by

 $\begin{eqnarray} T_{\sigma}(E, V)=Tr[\Gamma_{\textrm{L}}G_{\sigma}\Gamma_{\textrm{R}}G_{\sigma}^{+}] \end{eqnarray}$ (1)

where $\sigma$ stands for the spin-up ($\uparrow$) and spin-down ($\downarrow$) channels. $G_\sigma$ is the spin-dependent retarded Green's function of the extended molecule, $\Gamma_{\textrm{L/R}}$ is the coupling matrix between the extended molecule and the left/right electrode. The current through the molecular junction is obtained by

 $\begin{eqnarray} I(V)=\frac{e}{h}\int T_{\sigma}(E, V)[f(E-\mu_{\textrm{L}})-f(E-\mu_{\textrm{R}})]\textrm{d}E \end{eqnarray}$ (2)

here, $e$ is the electron charge, $h$ is the Planck constant, $f_{\textrm{L/R}}$ is the Fermi-Dirac distribution function for the left or right electrode, while $\mu_\textrm{L}$ and $\mu_\textrm{R}$ is the electrochemical potential for left and right electrodes, respectively.

Here, the current is calculated by using the Landauer-Büttiker formula, in which the spin-up and spin-down electrons are coherent, indicating that the length of the active channel is less than the phase-breaking mean free path.

Ⅲ. RESULTS AND DISCUSSION A. Free SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes

We begin with the geometric, electronic and magnetic properties of the free SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with HS and LS states. The initial geometric parameters for the examined Fe(Ⅱ)-N$_4$S$_2$ complexes with the HS and LS states are taken from the experimental X-ray crystallography results [26]. In the examined magnets, two thiol, serving as anchoring groups to Au electrodes in the following transport calculations are decorated at the end of pyridine ligands [29-31]. The optimized structures of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with HS and LS states are shown in FIG. 1 (a) and (b), respectively. It is clear that the Fe-N and Fe-S distances around Fe(Ⅱ)-N$_4$S$_2$ coordination core with the HS and LS states are quite different, which vary from 1.98 Å to 2.53 Å, and from 1.93 Å to 2.21 Å, respectively. The bond-length differences for two different spin-states fall within the range of [0.05, 0.40] Å. The averaged bond length with the HS state is about 0.2 Å longer than that of LS case. The relative longer Fe-N and Fe-S distances in pseudo-octahedral coordination lead to the local relatively weak Fe(Ⅱ)-N$_4$S$_2$ crystal field, corresponding to the HS state. The 3d$^6$ electrons of Fe(Ⅱ) core in the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with the HS and LS states can be described by t$^6_{2\textrm{g}}$e$^0_\textrm{g}$ and t$^4_{2\textrm{g}}$e$^2_\textrm{g}$ electron configurations, and correspond to singlet (S=0) and quintet (S=2) spin-states, respectively. The corresponding magnetic moments of the Fe(Ⅱ)-N$_4$S$_2$ complexes of HS and LS are predicted to be 0.0 and 4.0 μ$_\textrm{B}$ (Bohr magneton). The spin density distribution, as shown in FIG. 1(b), indicates that the magnetic moment of the Fe(Ⅱ)-N$_4$S$_2$ complex with the HS state is mainly contributed by the Fe(Ⅱ) ion. The calculated total energies show that the ground state of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complex is the LS state, and the corresponding energy is lower about 1.02 eV than that of the HS one. Clearly, these optimized key structural parameters and predicted magnetic moments agree well with the experimental results [26].

As shown in FIG. 1(c), the spatial distribution of the frontier orbitals and their energy positions of the free SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with HS and LS states are totally different. As for the LS state, the ground state of this complex is nonmagnetic. The highest occupied molecular orbital (HOMO) locating at -0.92 eV mainly localizes around the Fe(Ⅱ) ion and two NCBH$_3$$^- ligands, while the lowest unoccupied molecular orbital (LUMO) lying at 0.89 eV distributes around the Fe(Ⅱ) ion and pyridyl ligands. As for the HS state, the complex is spin-polarized, and the spin-up and spin-down electrons display different features. The HOMO (-0.94 eV) and LUMO (1.15 eV) of the spin-up electrons mainly localize around the ligands, which is composed of two S functional framework, while the HOMO (-0.01 eV) and LUMO (0.45 eV) of the spin-down electrons mainly localize around the two pyridyl ligands and Fe(Ⅱ) ion. That is to say, the energy gap between the HOMO and LUMO of the spin-up and spin-down channels are predicted to be 2.09 and 0.46 eV, respectively. This result suggests that the spin-down electrons maybe more easily pass through the SCO magnet Fe(Ⅱ)-N_4S_2 complex than that of the spin-up electrons. These observed remarkably differences in the geometric and electronic structures of the SCO magnet Fe(Ⅱ)-N_4S_2 complexes with two different spin-states suggest that they are possible candidates for designing molecular spintronics devices with different transport behaviors. B. SCO transition barriers Before investigating the transport properties of the SCO magnet Fe(Ⅱ)-N_4S_2, we turn to estimate the SCO transition barriers switching between the HS and LS states, since the experimental and theoretical investigations have revealed that the SCO magnet Fe(Ⅱ)-N_4S_2 can be photoswitched between two different spin-states. The calculated total energies of the isolated SCO magnet Fe(Ⅱ)-N_4S_2 complexes with the HS and LS states as a function of the reaction coordination (X) are plotted in FIG. 2. Here, the value of X is interpolated between the LS (X=0) and the HS (X=1) geometry for two different spin-states. It is clear that the ground state of the SCO magnet Fe(Ⅱ)-N_4S_2 complex is the LS state. With increasing of X, due to the gradually weakening of the pseudo-octahedral crystal field, there is a transition from the LS to the HS at X$$\approx$0.6. Then, the energy barrier from the LS to the HS state transition is predicted to be 1.73 eV, while the reversal transition barrier, from the HS to the LS transition, is 0.71 eV. This result implies that the spin transition between the HS and LS states can be realized by light irradiation, which can also be used to understand the experimental observations. Under the white light irradiation, a similar SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complex can be switched from the LS to the HS state at very low temperature of 4.2 K [26].

 FIG. 2 The relative total energies of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with the LS and HS states along the reaction coordinates ($X$).
C. Transport properties

To explore the transport properties, here, as examples, the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with the HS and LS states are sandwiched between two Au(111) electrodes, which are modeled with (6$\times$6) supercells using the periodic condition. Through calculating the adsorption energies, we find that the CO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes prefer to adsorb on the hollow sites of Au(111) surface via Au-S bonds, as shown in FIG. 3(a). The proposed two-probe systems can be divided into three parts, including the left and right electrodes, and the central extended molecule containing the sandwiched SCO magnet Fe(Ⅱ)-N$_4$S$_2$ and two and three surface layers of the left and right electrodes, respectively, where all the screening effects are included into the contact region, and charge distribution in the electrodes is the same as that of the bulk phase. Here, the Au-S distance is optimized to be about 2.1 Å, which is close to the adopted value in the previous investigations. Firstly, we calculate the zero-bias transmission coefficients of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ with the LS state, and plot them in FIG. 3(b). Clearly, there is a broad transmission peak locating around -0.2 eV, while a narrow and small transmission peak appears at 1.8 eV. They are contributed by the perturbed HOMO and LUMO, respectively, since they accord well with the predicted molecular projected self-consistent Hamiltonian (MPSH) eigenvalues, labelled with the empty triangles at -0.11 and 2.02 eV in FIG. 3(b), respectively. Here, the MPSH eigenstates can be referred as perturbed molecular orbitals (MOs) because of the presence of Au electrodes. It is clear that in the energy window from -0.1 eV to 1.5 eV, the transmission coefficients are negligible. This observation implies that the current through the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ with the LS state under the small bias voltages will be small.

 FIG. 3 (a) Schematic illustration of the proposed SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction, here, the Fe(Ⅱ)-N$_4$S$_2$ molecule connect to two Au(111) electrodes with periodic condition. Here, the yellow, blue, luminous, orange, pink, gray, and white balls stand for Au, N, S, Fe, B, C, and H atoms, respectively. (b) Zero-bias transmission curve of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the LS state, in which the empty triangles stand for the perturbed HOMO and LUMO eigenvalues.

The calculated zero-bias transmission curves of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ with the HS state are plotted in FIG. 4. As we can see, it retains its spin polarization in the proposed junction. The energy positions of the perturbed MOs relative to the Fermi level match well with the transmission peaks. The remarkably difference of the conductance behavior of two spin channels is observed, which is expected due to the different electronic structures of the free HS magnet, as shown in FIG. 1(c). As for the spin-up (majority) electrons, there are two narrow transmission peaks below the Fermi level, while above the Fermi level the transmission coefficients are very small and the transmission spectrum shows flat feature. Upon the spin-down electrons, two narrow and significant transmission peaks locate at -0.05 and 0.35 eV, respectively. The distinct difference of transmission spectrum between two spin channels can be evaluated with spin filter efficiency (SFE) at the Fermi level, defined as:

 $\begin{eqnarray} \textrm{SFE}=\frac{T_{\uparrow}(E_\textrm{F})-T_{\downarrow}(E_\textrm{F})}{T_{\uparrow}(E_\textrm{F})+T_{\downarrow}(E_\textrm{F})} \end{eqnarray}$ (3)
 FIG. 4 Zero-bias transmission spectra of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state for the spin-up (black line) and spin-down (red line) electrons. In which the empty triangles stand for the perturbed HOMO and LUMO eigenvalues.

Here, $T_{\uparrow}$ and $T_{\downarrow}$ stand for the transmission coefficient of the spin-up and spin-down electrons, respectively. The positive SFE denotes a conductance dominated by the spin-up channel, while the negative one indicates that the spindown channel dominate. $T_{\uparrow}$ and $T_{\downarrow}$ at the zero bias of 5 V through the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state is 1.1$\times$10$^5$ and 0.15 G$_0$ (G$_0$ denotes the quantum conductance), respectively. It turns out the calculated SFE at zero bias is about 99.98%, indicating that conductance through the molecular junction is mainly governed by the spin-down electrons under the small bias voltage. This low-bias transport properties governed by the spin-down electrons have been observed in C$_{28}$ molecular junction and SCO magnet Fe$_2$ complex with the [HS-HS] spin-pair configuration [32, 33].

FIG. 5(a) shows that calculated spin-resolved - curves of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state in the bias voltage ($V_\textrm{b}$) range from -0.4 V to 0.5 V. Here, the current of spin-up and spin-down electrons is plotted with the black and red lines, respectively. At each bias voltage, the current is determined self-consistently under the non-equilibrium condition. We find that the - curves of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ with the HS state sandwiched between two Au(111) electrodes under finite bias voltages displays obvious spin-filtering effect. Within the examined $V_\textrm{b}$ range, the current of the spin-down electrons ($I_{\downarrow}$) through the molecular junction is remarkably larger than that of spin-down electrons ($I_{\uparrow}$). For example, the $I_{\uparrow}$ at 0.4 V is close to 0.0 $\mu$A, which is significantly less than the corresponding $I_{\downarrow}$ values (0.67 $\mu$A). This observed spin-filtering feature can be easily understood according to the calculated transmission spectra (see FIG. 4).

 FIG. 5 (a) The Ⅰ-Ⅴ curves of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state for the spin-down (red line) and spin-up (black line) electrons. (b) The Ⅰ-Ⅴ curves of the pro-posed junctions with the HS (red line) and LS (black line) states.

To compare the conductivity of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with two different spin states, the currents for the HS and LS states are plotted in FIG. 5(b) with the red and black lines, respectively. It is clear that the current ($I_{\textrm{HS}}$) through the magnet junction with the HS state is larger than that of the LS state ($I_{\textrm{LS}}$). For example, at 0.2 V, the $I_{\textrm{HS}}$ is predicted to be 0.57 $\mu$A, mainly contributed by the spin-down electrons, while the $I_{\textrm{LS}}$ is 0.10 $\mu$A. This result implies that the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes could act as a molecular switch when the spin transition is triggered in this magnet by external stimuli, i.e. light.

To compare the conductivity of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with two different spin states, the currents for the HS and LS states are plotted in FIG. 5(b) with the red and black lines, respectively. It is clear that the current ($I_{\textrm{HS}}$) through the magnet junction with the HS state is larger than that of the LS state ($I_{\textrm{LS}}$). For example, at 0.2 V, the $I_{\textrm{HS}}$ is predicted to be 0.57 $\mu$A, mainly contributed by the spin-down electrons, while the $I_{\textrm{LS}}$ is 0.10 $\mu$A. This result implies that the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes could act as a molecular switch when the spin transition is triggered in this magnet by external stimuli, i.e. light.

Note that, in molecular electronic the exact anchoring configuration of molecular devices in experiments is a "blackbox" so far [7, 18]. Here, we also examine the transport properties of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with the HS and LS states using Au nanoelectrodes. The calculated - curves are plotted in FIG. 6. We observe the similar results. That is to say, the current through the magnet junction with the LS state is still less than that of the HS state. As for the junction with the HS state, the current is also mainly contributed by the spin-down electrons, which results in a high SFE of 72.00%. Clearly, the transport properties through the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ junction with two different spin states are not sensitive to the adopted Au electrodes. This observation highlights the potential applications of this kind of SCO magnets in molecular spintronics.

 FIG. 6 The Ⅰ-Ⅴ curves of SCO magnet Fe(Ⅱ)-N$_4$S$_2$ sandwiched between two Au nanoelectrodes.
Ⅳ. CONCLUSION

In summary, based on DFT calculations combined with NEGF technique, we explore the electronic and transport properties of the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes with the HS and LS states. We clearly reveal that the spin transition between the HS and LS states can be achieved by visible light irradiation. The SCO magnets Fe(Ⅱ)-N$_4$S$_2$ junction with the HS state has high spin filtering efficiency. Under a small bias voltage, the current through the HS SCO magnets Fe(Ⅱ)-N$_4$S$_2$ is mainly contributed by the spin-down electrons, and the current is larger than that of the LS case. Theoretical findings suggest that the SCO magnet Fe(Ⅱ)-N$_4$S$_2$ complexes hold the great promising applications in molecular electronic devices.

Ⅴ. ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No.21473168 and No.11634011) and the Innovative Program of Development Foundation of Hefei Center for Physical Science and Technology. Computational resources have been provided by the CAS, Shanghai and USTC Supercomputer Centers.

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Fe（Ⅱ）-NH(aΔ)N4S2自旋翻转单分子磁体的电子输运性质

a. 中国科学技术大学, 合肥微尺度物质科学国家研究中心, 合肥 230026;
b. 安徽建筑大学材料与化工学院, 合肥 230601